How does observing the breath lead to peace?
Q: How is it that focusing on the moment, on the breath or other neutral object in meditation brings peace, happiness, cures, and the like?
A: Focusing and refocusing on the breath or other neutral object in meditation is a practice that over time trains the mind to remain mindful of present-moment activity and to recognize and let go of the conditioned and spontaneous thoughts, feelings, and sensations to which we usually react impulsively. Learning to simply let go when appropriate in daily activity of such negative thoughts and feelings rather than denying or resisting them or compulsively dwelling upon, indulging, or acting them out is what enables us to experience more peace and happiness within ourselves and more lovingkindness and compassion toward others.
From a Buddhist perspective, lovingkindness, compassion, joy, and equanimity (peacefulness) are innate virtues obscured by conditioned patterns of negative thoughts, speech, and behavior. Learning to recognize and let go of these negative patterns enable these innate positive qualities to emerge. This is the basis for the oft repeated phrase: "You're already enlightened, you just don't realize it." Meditation is perhaps the most powerful practice leading to the realization of your already enlightened nature and that you are not the conditioned egoic patterns with which you have mistakenly identified. If interested, you might read my "What is Enlightenment" article, listed on the right under "Articles."